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Upper and Lower Bounds in Relator Spaces

Száz, Árpád (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 06A06, 54E15An ordered pair X(R) = ( X, R ) consisting of a nonvoid set X and a nonvoid family R of binary relations on X is called a relator space. Relator spaces are straightforward generalizations not only of uniform spaces, but also of ordered sets. Therefore, in a relator space we can naturally define not only some topological notions, but also some order theoretic ones. It turns out that these two, apparently quite different, types of notions are closely...

α -ideals in 0 -distributive posets

Khalid A. Mokbel (2015)

Mathematica Bohemica

The concept of α -ideals in posets is introduced. Several properties of α -ideals in 0 -distributive posets are studied. Characterization of prime ideals to be α -ideals in 0 -distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal I of a 0 -distributive poset is non-dense, then I is an α -ideal. Moreover, it is shown that the set of all α -ideals α Id ( P ) of a poset P with 0 forms a complete lattice. A result analogous to separation theorem for finite 0 -distributive...

λ -lattices

Václav Snášel (1997)

Mathematica Bohemica

In this paper, we generalize the notion of supremum and infimum in a poset.

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